We use the finite limit approximation to the beta process [1]}, [2]}. For \(\pi _k \sim \mathrm {Beta}\left(\alpha \gamma / K, \alpha \left( 1- \gamma \ K \right)\right)\)  and
\(\Phi _k \sim g(\cdot )\) , the random measure \(H_K = \sum _{k=1}^{K} \pi _k \delta _{\Phi _k}\) , \(\lim _{K\rightarrow \infty } H_K\)  converges in distribution to \(H \sim BP(\alpha , \gamma )\) . In addition, for \(z_{nk} \sim \mathrm {Bern}(\pi _k)\) , where \(\pi _k \sim \mathrm {Beta}\left(\alpha \gamma / K, \alpha \left( 1- \gamma \ K \right)\right)\) , \(k= 1,\ldots ,K\) , the random measure \(G_{n}^{K} = \sum _{k=1}^{K} z_{nk} \delta _{\Phi _k}\) , \(\lim _{K\rightarrow \infty } G_{n}^{K}\)  converges to a Bernoulli process [3]}.
